i need to sketch a graph that satisfies all of these conditions:

Question

- it is defined for all #s except 0

- f(1) = 0 f(2)=2 f(3)=1

- f'(2)=0 f''(3)=0

- f''(x)<0 when x<0 and when 0<x<3

- f''(x)>0 when x>3

- lim x->0 = -inf

- lim x->inf = 0

- lim x->-inf = 2

sorry about the organization, hope you can help!

I cant sketch here. Locate the points first, then sketch at those points the slope lightly, then note the points of infliction, when the curvature changes. The outside limits next, sketch those, then fill in all in between.